The objective of this work was to develop a display of speech signals that provides useful, visually extractable information supplementary to that apparent in spectrograms. The approach was to develop and analyze pitch-synchronous displays of the acoustic pressure wave in which successive pitch intervals of voiced speech are time-aligned and closely spaced. Methods were developed for automated and semi-automated epoch extraction, based upon the nearest-neighbor algorithm and extrapolations from pitch-period contours. Theoretical studies relevant to such displays included the effects of the fundamental frequency of vocal fold oscillation on the time waveform, the effects of locally zeroing the spectral phase of time signals, and the mathematical relationship existing between spectrograms and pitch-synchronous time-domain displays. Through a known generalization of Shannon's sampling theorem, it was shown that the line spectrum of voiced speech is generally an undersampled version of the spectral envelope associated with a given vocal tract configuration; using a theorem by Linden and Abramson, conjectures were developed on ways that listeners might use the "jitter" normally found in speech to compensate for such undersampling and to aid constancy in perception of a vowel's identity as it is heard at different pitches.